The division problem under constraints consists of allocating a given amount of an homogeneous and perfectly divisible good among a subset of agents with single-peaked preferences on an exogenously given interval of feasible allotments. We characterize axiomatically the family of extended uniform rules proposed to solve the division problem under constraints. Rules in this family extend the uniform rule used to solve the classical division problem without constraints. We show that the family of all extended uniform rules coincides with the set of rules satisfying eficiency, strategy-proofness, equal treatment of equals, bound monotonicity, consistency, and independence of irrelevant coalitions.

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We thank two anonymous referees for their extremely valuable comments. The work of G. Bergantiños is partially supported by research grants ECO2008-03484-C02-01 and ECO2011-23460 from the Spanish Ministry of Science and Innovation and FEDER. J. Massó acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2011-0075) and through grant ECO2008-0475-FEDER (Grupo Consolidado-C), and from the Generalitat de Catalunya, through the prize ICREA Academia for excellence in research and grant SGR2009-419. The work of A. Neme is partially supported by the Universidad Nacional de San Luis, through grant 319502, and by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), through grant PIP 112-200801-00655.